The no-go theorem for observer-independent facts by Brukner [1]} was actually introduced earlier than  [2]} in a similar effort to prove that measured facts are observer-dependent. The experimental setup is shown in Figure REF . In  [1]}, there are only two different measurement setups either Alice or Bob will perform, compared to three different measurement setups in  [2]}. Furthermore, the way the no-go theorem in is proved is different. The proof in  [1]} leverages the well-known Bell-CHSH inequality thus inherits all the assumptions associated with the Bell-CHSH theorem, while the no-go theorem in  [2]} is proved independent of Bell-CHSH theorem. As we will explain next, the proof in [1]} is more subtle, as it carefully chooses a quantum state and a set of measurement operators such that the law of total probability holds true if only considering Alice's (or Bob's) measurements.
